In constructing truth-tables we start with the truth table for disjunction (∨).
|A||B||A ∨ B||¬(A ∨ B)||¬A||¬B||¬A ∨ ¬B|
To get the truth table for ¬(A ∨ B) we merely need to flip the truth-values of the truth-table for (A ∨ B).
By contrast, if we want the truth-table for ¬A ∨ ¬B, we need to start with truth-tables for ¬A and for ¬B.
We then combine these two truth tables using disjunction -- so it's True whenever ¬A is True or ¬B is True, and False otherwise.
Now focus just on the truth tables for our two sentences, one with negation inside the brackets the other with negation outside the brackets
The truth of the first denial sentence, ¬(A ∨ B), guarantees that you're alive (B = 'I am dead'), whereas the truth of the second denial, ¬A ∨ ¬B, doesn't entail that you're alive.
Sometimes students decide they'll ignore brackets and hope for the best. But the difference between putting the negation outside of parenthesis and putting into individual brackets is a matter of life or death.